Some important questions can't be asked without sounding crass and insensitive. But there's no way around asking this one that's on everybody's mind, so here goes:

What is Apple Inc.'s plan if Chief Executive Steve Jobs dies?

The question of Jobs' health has been a live discussion thread since he announced in August 2004 that he had undergone surgery for pancreatic cancer. When Apple announced a few weeks ago that -- for the first time since his return to the Cupertino, Calif., company in 1997 -- he wouldn't deliver the keynote address Tuesday at the annual Macworld exposition in San Francisco, the chatter was reenergized for the umpteenth time.

Apple said a Jobs underling would give the keynote. It claimed that the change didn't have anything to do with its CEO's health. Instead, it said it didn't care about Macworld any longer because it had better ways to communicate with its faithful than by featuring its famous CEO at a big event where it had rolled out major products year after year.

Right.

With almost every Jobs health scare, Apple's stock has dropped a couple of percentage points. That happened in June, when he appeared at a Mac developers' conference looking thin and pale ("a common bug," the company said) and in August, when Bloomberg News briefly flashed his obituary on the wires by mistake. One day last week, when an especially pessimistic report on his health was posted online, Apple shares were taken down nearly 4% in a straight line. (They recovered about half the loss by day's end.)

One reason for the market's anxiety -- Apple shares shed more than 56% in 2008 -- is that the company has been silent about its succession plan. It says it has one but won't disclose it.

Yet a corporate succession plan is like the Soviet Doomsday Machine in "Dr. Strangelove": It's useless unless you announce it to the world. The idea is to give investors, employees, customers and suppliers confidence that there won't be an extended period of turmoil while executives jockey with one another, switchblades at the ready, to fill the void.

Persistent confusion about a company's succession often hints at a pathology at the top. Viacom's 85-year-old chairman, Sumner Redstone, who has made it clear he expects to remain in place longer than the half-life of plutonium-239 (spot-quiz answer: 24,100 years), has seen off a parade of would-be successors.

There were Mel Karmazin and Tom Freston and even his own daughter, Shari -- each one at first lauded by Papa Doc Redstone, then humiliated on their paths out of favor. And who can forget the thrill ride staged by Disney's Michael Eisner, who stretched out his retirement saga for more than two years?

No American CEO is more intimately identified with his company's success. Jobs is deeply involved in every facet of Apple development and design, and he's justly admired for his instinct for the human-factor engineering of Apple products. He is Apple's visionary and carnival barker.

If you want a taste of the latter persona, watch the video of the original iPod launch event in October 2001. Jobs' dramatic command is astonishing -- viewing the event recently on Youtube, I was on the edge of my seat, even though I knew how the story came out.

The Jobs role that Apple may find hardest to fill is that of one-man Supreme Court, settling disputes between warring engineering camps by decree. There have been countless battles at Apple over such things as how many buttons a mouse should have and what keys should be on its keyboards. The ultimate authority belongs to Jobs.

Many Apple watchers say the executive team backing up Jobs will have no trouble carrying on without him. Several internal candidates for leadership look like partial Jobs clones. Tim Cook, Apple's chief operating officer and head of manufacturing, is said to embody his perfectionism and competitive ferocity. Jonathan Ive has been responsible for the physical design of such trend-setting products as the candy-colored iMacs of the late 1990s and the sleek version of today, as well as the iPod.

"Jobs' way of doing things has been institutionalized there," Leander Kahney, news editor of wired.com and author of three books about Apple, told me recently. "He could go away for several weeks, even a year, and things would work. He's created a machine that will keep ticking over."

That sounds like wishful thinking. There are signs that the company is nearing inflection points in several of its product lines that could make it especially vulnerable to management turmoil.

Mac mavens are starting to grouse about the computer's lengthening product cycle, meaning that the time between upgrades is getting longer. The iPod in its traditional form has pretty much run out its string. Speaking as the owner of four iPods, I must say it's been more than a year since I've seen a new version I felt I had to run out and buy, and that's an eon in iPod time.

Apple's signature product is now the iPhone, but that's not as comforting for Apple fans as it should be. For one thing, the iPhone is tied to AT&T's lame and overpriced wireless network. For another, it's feeling the warm breath of numerous rivals on its tail feathers -- particularly Google and its Android mobile phone operating system.

Apple may surprise everybody at Macworld. A hale Jobs might appear after all, or the company might unveil a jaw-dropping product. But that wouldn't eradicate the flaws in Apple's approach to the question of Jobs' health, which has always been to dismiss the issue as a "private matter."

That's not so when we're talking about a CEO whose talents and personality are so inextricably entwined with a signature American brand. As an admirer of both, I hope the day when Apple has to contemplate life without Steve Jobs stays far, far in the future. But the value of the company and the perception of its future are now tied, at least in the short term, to the public perception of his future.

Isn't it time he and Apple confronted the questions head on?

Michael Hiltzik's column appears every Monday and Thursday. He can be reached at michael.hiltzik @latimes.com.